Finite-band solitons in the Kronig-Penney model with the cubic-quintic nonlinearity.
Finite-band solitons in the Kronig-Penney model with the cubic-quintic nonlinearity.
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DOI：
10.1103/physreve.71.016613
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发表时间：
2005
期刊：
影响因子：
--
通讯作者：
I. Merhasin;B. Gisin;R. Driben;B. Malomed
中科院分区：
文献类型：
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作者：
I. Merhasin;B. Gisin;R. Driben;B. Malomed
我们提出了一个结合周期性矩形势阱阵列[kroning - penney （KP）势]和三次五次（CQ）非线性的模型。在系统中发现了大量的孤子态：基本单峰孤子，对称和反对称双峰孤子，峰间有或没有相移pi的三峰孤子，等等。如果势剖面较浅，则孤子属于线性KP模型带结构下的半无限隙，而布洛赫带之间的有限隙仍然为空。然而，与周期势和自聚焦Kerr非线性相结合的模型中已知的情况相反，孤子仅填充半无限隙顶部附近的有限区域，这是CQ非线性的饱和特性的结果。如果势结构更深，那么在有限间隙中就会发现具有平顶形状的基本孤子和双孤子（对称和反对称）。小扰动稳定性特征值的计算和直接模拟表明，所有孤子都是稳定的。在浅KP势中，以积分功率Q（或宽度w）与传播常数k的形式表示的孤子特性显示出很强的双稳性，对于给定的k，可以找到两个，有时是四个不同的解（双稳性随着势的深度增加而消失）。不符合Vakhitov-Kolokolov判据，dQ/dk >和dQ/dk < 0的解分支是稳定的。曲线Q(k)对应于每一种特定类型的解（具有给定数量的局部峰和确定的对称性）在Q的有限最大值处结束（在端点之后发现呼吸者）。积分功率的增加会在孤子的形状上产生额外的峰，每个峰对应于一个被困在KP结构的局部通道中的子脉冲（一种分束特性）。这是合理的，这些特征是由其他模型结合了可饱和非线性和周期性衬底共享。
We present a model combining a periodic array of rectangular potential wells [the Kronig-Penney (KP) potential] and the cubic-quintic (CQ) nonlinearity. A plethora of soliton states is found in the system: fundamental single-humped solitons, symmetric and antisymmetric double-humped ones, three-peak solitons with and without the phase shift pi between the peaks, etc. If the potential profile is shallow, the solitons belong to the semi-infinite gap beneath the band structure of the linear KP model, while finite gaps between the Bloch bands remain empty. However, in contrast with the situation known in the model combining a periodic potential and the self-focusing Kerr nonlinearity, the solitons fill only a finite zone near the top of the semi-infinite gap, which is a consequence of the saturable character of the CQ nonlinearity. If the potential structure is much deeper, then fundamental and double (both symmetric and antisymmetric) solitons with a flat-top shape are found in the finite gaps. Computation of stability eigenvalues for small perturbations and direct simulations show that all the solitons are stable. In the shallow KP potential, the soliton characteristics, in the form of the integral power Q (or width w) versus the propagation constant k, reveal strong bistability, with two and, sometimes, four different solutions found for a given k (the bistability disappears with the increase of the depth of the potential). Disobeying the Vakhitov-Kolokolov criterion, the solution branches with both dQ/dk > 0 and dQ/dk < 0 are stable. The curve Q(k) corresponding to each particular type of the solution (with a given number of local peaks and definite symmetry) ends at a finite maximum value of Q (breathers are found past the end points). The increase of the integral power gives rise to additional peaks in the soliton's shape, each corresponding to a subpulse trapped in a local channel of the KP structure (a beam-splitting property). It is plausible that these features are shared by other models combining saturable nonlinearity and a periodic substrate.